How generation intervals shape the relationship between growth rates and reproductive numbers

Proceedings of the Royal Society B: Biological Sciences - Tập 274 Số 1609 - Trang 599-604 - 2007
Jacco Wallinga1, Marc Lipsitch2
1Department of Infectious Diseases Epidemiology, National Institute of Public Health and the Environment, PO Box 1, 3720 BA Bilthoven, The Netherlands.
2Department of Epidemiology and Department of Immunology and Infectious Diseases, Harvard School of Public Health677 Huntington Avenue, Boston, MA 02115, USA

Tóm tắt

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive numberR. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rater. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number.

Từ khóa


Tài liệu tham khảo

Anderson R.M& May R.M Infectious diseases of humans: dynamics and control. 1991 Oxford UK:Oxford University Press.

Begon M Harper J.L& Townsend C.R Ecology. 1996 Oxford UK:Blackwell.

Caswell H Matrix population models: construction analysis and interpretation. 2nd edn. 2001 Sunderland MA:Sinauer Press.

Dublin L.I, 1925, On the true rate of natural increase, as exemplified by the population of the United States, 1920, J. Am. Stat. Assoc, 150, 305, 10.1080/01621459.1925.10503498

10.1214/aoms/1177731708

10.1038/nature04017

10.1038/nature04795

10.1038/414748a

10.1098/rsif.2005.0042

10.1016/j.ics.2004.02.020

10.1126/science.1065973

Keyfitz N& Caswell H Applied mathematical demography. 2005 New York NY:Springer.

10.1016/0025-5564(95)00053-4

10.1126/science.1086616

10.1093/aje/kwh092

Metz J.A.J& Diekmann O The dynamics of physiologically structured populations. 1986 Berlin Germany:Springer p. 153.

10.1038/nature03063

Mood A.M Graybill F.A& Boes D.C Introduction to the theory of statistics. 1974 Singapore:McGraw-Hill.

10.1126/science.1058321

10.1098/rspb.2003.2339

10.1093/aje/kwh255

10.1371/journal.pmed.0020174

Thông tin
Thông tin xuất bản

Proceedings of the Royal Society B: Biological Sciences

Tập 274 Số 1609

599-604

Thông tin tác giả